The values of x and y, if \(\begin{bmatrix}2x+y & 6\\ -1 & 3x+2y\end{bmatrix}=\begin{bmatrix}4 & 6\\ -1 & 7\end{bmatrix}\) are:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → x = 1, y = 2
Two matrices are equal when their corresponding entries are equal:
\(2x + y = 4 \quad (1)\)
\(3x + 2y = 7 \quad (2)\)
Multiplying (1) by 2 and subtracting (2):
\(4x + 2y - (3x + 2y) = 8 - 7\)
\(x = 1\)
From (1):
\(y = 4 - 2 = 2\)